A062688 Smallest triangular number with digit sum n (or 0 if no such number exists).

1, 0, 3, 0, 0, 6, 0, 0, 36, 28, 0, 66, 0, 0, 78, 0, 0, 378, 496, 0, 1596, 0, 0, 8385, 0, 0, 5778, 5995, 0, 8778, 0, 0, 47895, 0, 0, 67896, 58996, 0, 196878, 0, 0, 468996, 0, 0, 887778, 1788886, 0, 4896885, 0, 0, 5897895, 0, 0, 13999986, 15997996, 0, 38997696

Offset: 1

Author

Erich Friedman, Jul 04 2001

Keywords

• base
• nonn

Comments

From Jon E. Schoenfield, Dec 04 2021: (Start)

a(n) = 0 iff n == (2,4,5,7,8) mod 9.

Nonzero terms are not nondecreasing; e.g., a(9)=36 > a(10)=28.

(End)

Examples

			66 is the smallest triangular number with digit sum 12, so a(12)=66.
		

Links

• Jon E. Schoenfield, Table of n, a(n) for n = 1..168

Crossrefs

Cf. A000217, A007953, A055264, A068808.

Programs

Mathematica

(With[{tbl={#,Total[IntegerDigits[#]]}&/@Accumulate[Range[9000]]},Table[SelectFirst[ tbl,#[[2]] ==n&],{n,60}]]/.Missing["NotFound"]->{0,0})[[;;,1]] (* Harvey P. Dale, Aug 21 2024 *)

PARI

a(n) = if (vecsearch([2,4,5,7,8], n % 9), return (0)); my(k=1); while (sumdigits(k*(k+1)/2) != n, k++); k*(k+1)/2; \\ Michel Marcus, Dec 12 2021